When am I supposed to use cover?

I use it in A10S if people cant avoid some of the hits while im OT-ing, Also the tethered coeurl moment in Hullbreaker hard comes to mind during the first boss. Vault first boss the jumping moment.
I do have it macro-ed to Mouseover and a shout out in party chat to notify the healers " Covering <mo> ! <se.2>"

I also use it on WHM's whom spammed medica 2 and pulled aggro, this gives me time to safely take aggro off of them. (Generally happens while the HoT is ticking and boss is invulnerable...)

You really need to be quick to react with Cover, but it does have it's uses. If you're fast with it you can save lives, just like with a well timed clemency. Us pally's might not have the best DPS, but our utility is what makes us useful ;)

When you do a duty unsync carrying a newcomer without a healer and he's eating all the hurting mechanics :p

A10S, my OT WAR holmgangs the boss so he can DPS it without moving away, I still provoke the boss but cover him for the Boss's AOE attack so he doesn't die.

In A10S, outside of Gobslice Moncrops(the attack where you have to activate the spikes), all unavoidable aoe attacks in A10s are magical, not physical, so using cover in a10s to protect people from AOE is in most cases useless.
You can easily look it up in the logs, or just ask your BLM to test it with either manaward or manawall :o

Cover was awesome in t13 and titan ex. In a12s it's useful for the 8 adds. However, in general, you'll need to know who's gonna get hit with physical damage soon to use it effectively.

When you die. I prefer not to have to do the scathe (benny hill) dance for 3 minutes because you think you can get hate on everything after I've dropped 3-4 flares already and my friendly co dps is still trying to hit the highest hp mobs instead of picking off the lower hp ones to thin out the incoming damage after sleeping/picking nose/scratching butt, etc.. in a corner previously, leading to the formentioned tank death.

Cover is extremely niche, but it's not useless. If you want to take your Pld to the next level than you have to actively look for places where you can use it. In general, you'll find Cover to be most useful on:

• Any Physical AoE. tether, cleave, or line attack. Physical being the operative word here. Cover does not protect against magical dmg. That said, even if the dmg cannot be soaked, certain status afflictions can still be taken by the Pld if they used cover.
  
• Proxy-pulls on additional enemies. Most boss adds die to quickly to be worth trying to snare enmity on them. Moving risks your position, and using Shield Lob/Flash is a waste of Tp or Mp. That said, you can still cover whoever does grab aggro to protect them from the damage, assuming they stay in range.
  
• Stack and/or status soaks. Already touched on this one, but certain status afflictions (mostly vulnerability stacks) can be absorbed by the Pld instead of the intended target if the Pld Covers the hit. This is particularly useful in the off tank position when you can mitigate a hit for the main tank, but it can also come in handy during standard dungeon pulls if any bosses or mobs put out a status ailment on the party.
  
• Knock-backs that can be nullified with Tempered Will. This doesn't include all knock-backs, but anything that can be TW'd can also be covered. It's probably the least useful application of Cover, in my opinion, but it works.
  
• PvP. This is the biggest one, really. If you ever happen to stumble into the arena as a Pld, then it's good to know that Cover is a godsend. The duration is long enough to cover the bulk of a dps burst, so you basically save one life per use of Cover. Typically, this is reserved for your healer, but it can also be used offensively by covering a Dps to keep them alive long enough to secure a kill. You just have to make sure you use it at the right moment. Also, again, you have to remember that cover only protects against physical damage. If you're facing a Blm or Smn, than your covered target can still be snuffed.

That about covers it. Honestly, I get more use out of Cover than I do out of Tempered Will, but I only use it as much as I do because I actually look for times when it will be useful. My advice to you is to keep your eyes open whenever you run a new dungeon (or an old one), and think outside the box. It's very niche, but you'll be surprised at how often you can use it if you're not just looking for the obvious and are quick on the button.

I use Cover a lot in expert roulette. If a DPS or healer starts taking a lot of damage because they poked mobs or tossed a regen during my full pull I'll cover them at the destination so they stay alive while I regain threat. I also made macros to automatically target and cast on the group member of my choice. That makes a huge difference because I don't have to fumble with targeting and etc, I just smash the proper button and then tab back onto the mobs.

@OP,

You should use cover when there is a mechanic that deals physical damage to another party member, isn't aoe, and that you can't redirect to yourself via provoke to gain and keep hate. -- really don't need to do this in 90% of the game and probably can forget about it. As the real importance of cover is to really ignore some mechanic that is a pain in the ass for the group. Such as Titan "table flip" where he puts up vulnerability stacks on the MT. But if you're in that type of group, your party will probably let you know

all skills with uniqe & Niche uses (PLD's Cover for example) requires "COMMUNICATION", I can't count the number of times I've tried the same strategies I do with my RL friend (which we chat threw PSN by voice) with someone else & watch it eather fail or they do the "Normal" way anyway due to lack of communication by eather me or the party (if the party know's & wants my idea but "Replacement" OT/MT only joined after it was decided)

but since u may want example's of use points for Cover here:
A8-Brutal Justice's Dubble rocket punch (Hallowed + Cover on Co-Tank, negates mechanic when in "Crunch time")
A5-Twinkledinks move he uses when big on MT (Vulnerible stacks plus a stun at 4 stacks) norm is provoke him off to save Tank death (unless MT used Hallowed/living dead/holmgang) use cover instead, u get hit but u didn't have the vuln stacks did u
4-man dungeons-anytime u see u'r healer about to take physical dmg by AoE or Boss move & u know they'll die from it (dungeon fight without a healer sucks & most times leads to a wipe)